Hello,
I experienced a similar problem with the 1990 LS400 I have.
The problem is that the remote receiver that is located in the car is defective. Apparently this is a "known issue" with the 1st GEN LS models.
Someone had a thread about this same thing but I couldn't find it to put the link in.
In my opinion, you have two options:
Take it to Lexus and ask them to replace the remote receiver. This is going to set you back $500+ but you will be able to use the "original" key.
Buy an aftermarket Alarm / Remote Key / Trunk package for approximately $200 - $250 installed. In my case, I found a Viper system at Best Buy and had them put it in. This gave me Remote Start, Alarm, Remote Key, & Remote Trunk Release. For my situation, it just seems like a better deal since I didn't really care about using the original key and got the Remote Start capability also.
Hope that helps...